340 



MAGNETIC METHOD 



IChap. 8 



by an equivalent magnet of moment M in the symmetry axis of the cross 

 (see Fig. 8-26) and by substitution of 45° + 8 for the angle ?/. Then 

 from Di + Dz = 0, 



. . ^ 0.707M[H(sin a cos t — cos a) -{- Z sin t] + mga sin t , . 



0.707ilf [H(sin a cos 6 + cos a) -{- Z sin i] + mgd sin i ' 



Since tan 8 = (s' — So)/2f, we have for a horizontal axis of revolution, 

 (c = 7r/2), 



s - So ^ 0.707M(Z - H cos a) + mga 

 2f ~ 0.707M (Z + H cos a) + mg^ti ' 



which is the principal equation for the instrument. 



(8-366) 



Fig. 8-26. Magnetic system of Haalck universal magnetometer. 



After the magnetic meridian has been determined by a compass, the 

 instrument is oriented into the E-W position. If the reflected scale is 

 not in the field, the horizontal deflector underneath is adjusted accord- 

 ingly. Then 



s' - So _ 0.707MZ ± mga 

 ~^f 0.707MZ ± mgd 



(8-36c) 



With sufficient accuracy an average value of Z = Zo may be taken for the 

 Z in the denominator, so that 



s = 



2fM 



0.707MZo ± mgd 



(o.707Z ± ^^ , (8-36d) 



